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6540 Lecture Notes - Lecture 12: Test Statistic, Chi-Squared Distribution, 2Degrees

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lavenderhornet902

30 Jul 2018

School

University of Canberra

Department

University of Canberra

Course

Professor

Dr Sumaira Qureshi

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Document Summary

Chi-square test: chi-square test for independence, chi-square test using technology, assu(cid:373)ptio(cid:374)s a(cid:374)d (cid:272)o(cid:374)ditio(cid:374)s. Chi-square distribution: take o(cid:374)ly positi(cid:448)e (cid:448)alues a(cid:374)d are ske(cid:449)ed to the right, spe(cid:272)ified (cid:271)y its degrees of freedo(cid:373). De(cid:374)oted as xdf: the p-value is the area under the density curve of this chi- square distribution to the right of the value of the test statistic. Ha: the two variables are not independent: test statistic. Find the chi-square test statistic: decision rule. Compare this test statistic to a x2 distribution with df = (r - i)(c - 1), where r is number of rows and c is number of columns: conclusion. Chi-square calculations: the (cid:272)hi-square statistic is a measure of how far the observed counts in a two-way table are from the expected counts, the for(cid:373)ula for the statisti(cid:272) is (o(cid:271)ser(cid:448)ed (cid:272)ou(cid:374)t expected count)2 expected count. The values in each cell are counts (not percentages or measurements!: i(cid:374)dependence assumption.

Related Questions

(14 marks) Fortune magazine publishes a list of the world’s billionaires each year. We will examine the top 97 of the 1992 list. Their wealth, age, and geographic location (Asia, Europe, Middle East, United States, and Other) are reported. Wealth is a right-skewed variable, so we will consider the natural logarithm log wealth to be the response and will see if age and geographic location are predictors.

(a) (2 marks) Let

Ebe a variable that is 1 if the person is from Europe and 0 otherwise,

Mbe a variable that is 1 if the person is from the Middle East and 0 otherwise,

Obe a variable that is 1 if the person is from the “Other” region and 0 otherwise,

Ube a variable that is 1 if the person is from the United States and 0 otherwise.

State a linear model for the mean of log wealth that includes age and the above 4

geographic variables. Call this the full model.

(b) (5 marks) The SSY for these data is 28.3351 and the SSE from ﬁtting the full model

is 27.0461. Use this information to construct an ANOVA table. Your table should

include columns for Source, df, SS, MS and F, and should include rows for the model

(full model), residual and total.

(c) (2 marks) In addition to the full model, the reduced model that includes only an

intercept and age is ﬁt. What is the null hypothesis being considered by ﬁtting these

two models? (Refer to quantities deﬁned in your model.)

(d) (3 marks) The SSM from the reduced model is 59.7. Calculate an F-statistic to test the hypothesis of part (c). State the degrees of freedom for the F-distribution

you would compare this statistic to. (You do not need to calculate the p-value or actually test the hypothesis.)

(e) (1 mark) Using terminology from class, name the kind of Ftest that the statistic in part (d) corresponds to.

(f) (1 mark) If the null model for these data is compared to the model that includes an

intercept and age, what are the results?

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